Problem $2(5$ marks$).$ Consider a tank with a movable piston as shown in Fig. P$2.$ The Tank contains water at a Pressure of $350$ kPa and a Volume of $800$ L $.$ The water is cooled until the volume is halved and the pressure is $150$ kPa and temperature is $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Now, do the following:

Figure P$2$ Schematic for Problem $2$

a$)$ Determine the total mass of the water.

b$)$ Determine the initial temperature of the water.

c$)$ Show the process on a $\backslash ($ P$-$v $\backslash )$ diagram with respect to saturation lines.